Modular Theory in Operator Algebras
Title | Modular Theory in Operator Algebras PDF eBook |
Author | Serban Stratila |
Publisher | Cambridge University Press |
Pages | 461 |
Release | 2020-12-03 |
Genre | Mathematics |
ISBN | 1108489605 |
The first edition of this book appeared in 1981 as a direct continuation of Lectures of von Neumann Algebras (by Ş.V. Strătilă and L. Zsid ) and, until 2003, was the only comprehensive monograph on the subject. Addressing the students of mathematics and physics and researchers interested in operator algebras, noncommutative geometry and free probability, this revised edition covers the fundamentals and latest developments in the field of operator algebras. It discusses the group-measure space construction, Krieger factors, infinite tensor products of factors of type I (ITPFI factors) and construction of the type III_1 hyperfinite factor. It also studies the techniques necessary for continuous and discrete decomposition, duality theory for noncommutative groups, discrete decomposition of Connes, and Ocneanu's result on the actions of amenable groups. It contains a detailed consideration of groups of automorphisms and their spectral theory, and the theory of crossed products.
Modular Theory in Operator Algebras
Title | Modular Theory in Operator Algebras PDF eBook |
Author | Şerban Valentin Strătilă |
Publisher | Cambridge University Press |
Pages | |
Release | 2020-12-03 |
Genre | Mathematics |
ISBN | 1108966772 |
The first edition of this book appeared in 1981 as a direct continuation of Lectures of von Neumann Algebras (by Ş.V. Strătilă and L. Zsidó) and, until 2003, was the only comprehensive monograph on the subject. Addressing the students of mathematics and physics and researchers interested in operator algebras, noncommutative geometry and free probability, this revised edition covers the fundamentals and latest developments in the field of operator algebras. It discusses the group-measure space construction, Krieger factors, infinite tensor products of factors of type I (ITPFI factors) and construction of the type III_1 hyperfinite factor. It also studies the techniques necessary for continuous and discrete decomposition, duality theory for noncommutative groups, discrete decomposition of Connes, and Ocneanu's result on the actions of amenable groups. It contains a detailed consideration of groups of automorphisms and their spectral theory, and the theory of crossed products.
Modular Theory of Operator Algebras
Title | Modular Theory of Operator Algebras PDF eBook |
Author | Elizabeth Akehurst |
Publisher | |
Pages | |
Release | 1977 |
Genre | |
ISBN |
Aspects of Operator Algebras and Applications
Title | Aspects of Operator Algebras and Applications PDF eBook |
Author | Ara, Pere |
Publisher | American Mathematical Soc. |
Pages | 178 |
Release | 2011 |
Genre | Mathematics |
ISBN | 0821849050 |
The contents of this book cover K-theory for operator algebras, modular theory by example, modular theory for the Von Neumann algebras of local quantum physics, and much more.
Theory of Operator Algebras I
Title | Theory of Operator Algebras I PDF eBook |
Author | Masamichi Takesaki |
Publisher | Springer Science & Business Media |
Pages | 424 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461261880 |
Mathematics for infinite dimensional objects is becoming more and more important today both in theory and application. Rings of operators, renamed von Neumann algebras by J. Dixmier, were first introduced by J. von Neumann fifty years ago, 1929, in [254] with his grand aim of giving a sound founda tion to mathematical sciences of infinite nature. J. von Neumann and his collaborator F. J. Murray laid down the foundation for this new field of mathematics, operator algebras, in a series of papers, [240], [241], [242], [257] and [259], during the period of the 1930s and early in the 1940s. In the introduction to this series of investigations, they stated Their solution 1 {to the problems of understanding rings of operators) seems to be essential for the further advance of abstract operator theory in Hilbert space under several aspects. First, the formal calculus with operator-rings leads to them. Second, our attempts to generalize the theory of unitary group-representations essentially beyond their classical frame have always been blocked by the unsolved questions connected with these problems. Third, various aspects of the quantum mechanical formalism suggest strongly the elucidation of this subject. Fourth, the knowledge obtained in these investigations gives an approach to a class of abstract algebras without a finite basis, which seems to differ essentially from all types hitherto investigated. Since then there has appeared a large volume of literature, and a great deal of progress has been achieved by many mathematicians.
Introduction to Vertex Operator Algebras and Their Representations
Title | Introduction to Vertex Operator Algebras and Their Representations PDF eBook |
Author | James Lepowsky |
Publisher | Springer Science & Business Media |
Pages | 330 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 0817681868 |
* Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.
Vertex Operator Algebras and the Monster
Title | Vertex Operator Algebras and the Monster PDF eBook |
Author | Igor Frenkel |
Publisher | Academic Press |
Pages | 563 |
Release | 1989-05-01 |
Genre | Mathematics |
ISBN | 0080874541 |
This work is motivated by and develops connections between several branches of mathematics and physics--the theories of Lie algebras, finite groups and modular functions in mathematics, and string theory in physics. The first part of the book presents a new mathematical theory of vertex operator algebras, the algebraic counterpart of two-dimensional holomorphic conformal quantum field theory. The remaining part constructs the Monster finite simple group as the automorphism group of a very special vertex operator algebra, called the "moonshine module" because of its relevance to "monstrous moonshine."